I suspect it was intended to be an infantry-clearing emplacement. You know, from those fun experimental days of the Civil War!

For shooting at Paul Bunyan.

Commercial scale bird hunting

kingjackhammer has it right, it's a punt gun, meant to be strapped to a boat.

http://en.wikipedia.org/wiki/Punt_gun

It's less the largest shotgun, and more the smallest piece of naval artillery.

There is a condition even smaller than micropenis, called nanopenis. It was made for dudes with that.

I think a candiate for if not largest shotgun, then large shotgun that has actually been used in service would be the Russian KS-23, at least the original barrels were made from rejected 23mm barrels for anti-aircraft guns, is a 4-gauge by European measurements, a 6-gauge by US standards. And techincally it's a "carbine" because the barrel is rifled (though the civilian version is a smoothbore)

http://world.guns.ru/shotgun/rus/ks-23-e.html

Then there's the Nock Gun, several musket barrels welded together as a English Navy as an anti-boarding device, like a portable mitrailleuse. Only a few of the Royal Navy's largest, heaviest, and craziest could fire it without dislocating their shoulder. When fired down from the rigging it tended to set the sails on fire.

http://www.youtube.com/watch?v=5vKH9deJ56k

Scaled-down reproductions are popular.